H. Amann, Dual semigroups and second order linear elliptic boundary value problems, Israel J. Math, vol.45, pp.225-254, 1983.

, Highly degenerate quasilinear parabolic systems, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.18, issue.4, pp.135-166, 1991.

, Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems, in Function spaces, differential operators and nonlinear analysis (Friedrichroda, 1992), vol.133, pp.9-126, 1993.

, Linear and quasilinear parabolic problems, of Monographs in Mathematics, vol.I, 1995.

P. Biler, W. Hebisch, and T. Nadzieja, The Debye system: existence and large time behavior of solutions, Nonlinear Anal, vol.23, pp.1189-1209, 1994.

P. Biler and T. Nadzieja, Existence and nonexistence of solutions for a model of gravitational interaction of particles. I, Colloq. Math, vol.66, pp.319-334, 1993.

S. A. Chang and P. C. Yang, Conformal deformation of metrics on S 2, J. Differential Geom, vol.27, pp.259-296, 1988.

T. Cie?lak and C. Stinner, New critical exponents in a fully parabolic quasilinear Keller-Segel system and applications to volume filling models, J. Differential Equations, vol.258, pp.2080-2113, 2015.

J. Deneubourg, Application de l'ordre par fluctuationsà la description de certainesétapes de la construction du nid chez les termites, Insectes Sociaux, vol.24, pp.117-130, 1977.

H. Gajewski and K. Zacharias, Global behaviour of a reaction-diffusion system modelling chemotaxis, Math. Nachr, vol.195, pp.77-114, 1998.

D. Horstmann, The nonsymmetric case of the Keller-Segel model in chemotaxis: some recent results, NoDEA Nonlinear Differential Equations Appl, vol.8, pp.399-423, 2001.

, On the existence of radially symmetric blow-up solutions for the Keller-Segel model, J. Math. Biol, vol.44, pp.463-478, 2002.

D. Horstmann and G. Wang, Blow-up in a chemotaxis model without symmetry assumptions, European J. Appl. Math, vol.12, pp.159-177, 2001.

B. Hu and Y. Tao, To the exclusion of blow-up in a three-dimensional chemotaxis-growth model with indirect attractant production, Math. Models Methods Appl. Sci, vol.26, pp.2111-2128, 2016.

S. Ishida and T. Yokota, Blow-up in finite or infinite time for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type, Discrete Contin. Dyn. Syst. Ser. B, vol.18, pp.2569-2596, 2013.

. Ph and . Laurençot, Global bounded and unbounded solutions to a chemotaxis system with indirect signal production, Discrete Contin. Dyn. Syst. Ser. B, vol.24, pp.6419-6444, 2019.

X. Li, Global existence and boundedness of a chemotaxis model with indirect production and general kinetic function, Z. Angew. Math. Phys, vol.22, issue.117, p.pp, 2020.

Y. Li and J. Lankeit, Boundedness in a chemotaxis-haptotaxis model with nonlinear diffusion, Nonlinearity, vol.29, pp.1564-1595, 2016.

T. Nagai, T. Senba, and K. Yoshida, Application of the Trudinger-Moser inequality to a parabolic system of chemotaxis, Funkcial. Ekvac, vol.40, pp.411-433, 1997.

E. Nakaguchi, K. Noda, K. Osaki, and K. Uemichi, Global attractor for a two-dimensional chemotaxis system with linear degradation and indirect signal production, Jpn. J. Ind. Appl. Math, vol.37, pp.49-80, 2020.

A. Pazy, Semigroups of linear operators and applications to partial differential equations, vol.44, 1983.

J. A. Powell, T. Mcmillen, and P. White, Connecting a chemotactic model for mass attack to a rapid integro-difference emulation strategy, SIAM J. Appl. Math, vol.59, pp.547-572, 1999.

T. Senba and T. Suzuki, Parabolic system of chemotaxis: blowup in a finite and the infinite time, IMS Workshop on Reaction-Diffusion Systems, vol.8, pp.349-367, 1999.

C. Stinner, C. Surulescu, and A. Uatay, Global existence for a go-or-grow multiscale model for tumor invasion with therapy, Math. Models Methods Appl. Sci, vol.26, pp.2163-2201, 2016.

S. Strohm, R. C. Tyson, and J. A. Powell, Pattern formation in a model for mountain pine beetle dispersal: linking model predictions to data, Bull. Math. Biol, vol.75, pp.1778-1797, 2013.

Y. Tao and M. Winkler, Boundedness in a quasilinear parabolic-parabolic Keller-Segel system with subcritical sensitivity, J. Differential Equations, vol.252, pp.692-715, 2012.

, Critical mass for infinite-time aggregation in a chemotaxis model with indirect signal production, J. Eur. Math. Soc. (JEMS), vol.19, pp.3641-3678, 2017.

Y. Tian, D. Li, and C. Mu, Stabilization in three-dimensional chemotaxis-growth model with indirect attractant production, C. R. Math. Acad. Sci, vol.357, pp.513-519, 2019.

P. White and J. Powell, Spatial invasion of pine beetles into lodgepole forests: a numerical approach, SIAM J. Sci. Comput, vol.20, pp.164-184, 1998.

, France E-mail address: laurenco@math.univ-toulouse, Toulouse Cedex, vol.9

, D-64289 Darmstadt, Germany E-mail address: stinner@mathematik.tu-darmstadt, Fachbereich Mathematik, Schlossgartenstr, vol.7